Unless I'm getting my history wrong I believe there is a brief coverage of the katana and other weapons in the original ju-jitsu curriculum.
As original Ju-jitsu and Judo used to be taught as the same martial art. Which was the standard for warriors back in the days of feudal Japan.

So it encompassed most everything that you would need to know about fighting. Which included weapons.

Brazilian Ju-Jitsu doesn't teach any of the weapons, but standard Ju-Jitsu should when you get up into the higher belts.

I'd do the usual Bullshido style check on any JJ school that teaches weapons. As has been pointed out JJJ did originate from the Samurai and some modern schools teach weaponry as well as their unarmed stuff, and are good at it but the majority I've seen/experienced aren't.

If you're after a specific Japanese weapon art you might want to try Naginata Do, Kendo, Jodo or Iaido.

Ju Jitsu arts teach defense from a sword attack, or how to use other tools to restrain an angry Samurai that has a sword, not so much as fighting with a sword. (Source: Greg Fernandez, Jundokai)
In my opinion, using a Katana is a lifelong (specialized) study. Otherwise take fencing or visit with the SCA.